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2 years ago

Express in simplest radical form. 24

Mathematics

1 answer:

Shalnov [3]2 years ago

6 0

Answer:

2√6

Step-by-step explanation:

√24

√24 can be split into √8 and √3 because 8x3=24

√8 can be split into √4 and √2, and √4 equals 2.

√3 times √2 is √6

2√6

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How much longer is the hypotenuse of the triangle than its shorter leg?

RUDIKE [14]

This is an incomplete question, here is a complete question and image is also attached below.

How much longer is the hypotenuse of the triangle than its shorter leg?

a. 2 ft

b. 4 ft

c. 8 ft

d. 10 ft

Answer : The correct option is, (b) 4 ft

Step-by-step explanation:

Using Pythagoras theorem in ΔACB :

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$(AB)^2=(AC)^2+(BC)^2$

Given:

Side AC = 6 ft

Side BC = 8 ft

Now put all the values in the above expression, we get the value of side AB.

$(AB)^2=(6)^2+(8)^2$

$AB=\sqrt{(6)^2+(8)^2}$

$AB=10ft$

Now we have to calculate the how much longer is the hypotenuse of the triangle than its shorter leg.

Difference = Side AB - Side AC

Difference = 10 ft - 6 ft

Difference = 4 ft

Therefore, the 4 ft longer is the hypotenuse of the triangle than its shorter leg.

5 0

3 years ago

Read 3 more answers

Write an algebraic expression for the situation.

natali 33 [55]

Answer:

28/d is the answer from my side

6 0

3 years ago

Carlos and Maria drove a total of 217 miles in 4.1 hours. Carlos drove the first part of the trip and averaged 52 miles per hour

VMariaS [17]

M = hours driven by Maria

c = hours driven by Carlos

since we know that Carlos was driving at an average of 52 mph, then in 1 hour he drove 52 miles, in 2 hours he drove 2*52 miles in "c" hours he drove c*52 miles or 52c.

Maria on the other hand is faster and does 54 mph, in 1 hour she does 1 * 54 miles, and on 2 hours she does 2 * 54 miles and in "m" hours she does m * 54 miles or 54m.

now, we know the total amount of miles they both drove is 217, so whatever "m" and "c" are we know that 54m + 52c = 217.

we also know it took 4.1 for the whole trip, so m + c = 4.1.

$\bf \begin{cases}
m+c=4.1\implies \boxed{c}=4.1-m\\
54m+52c=217\\
-------------\\
54m+52\left( \boxed{4.1-m} \right)=217
\end{cases}
\\\\\\
54m-52m+213.2=217\implies 2m=3.8
\\\\\\
m=\cfrac{3.8}{2}\implies m=1.9$

so Maria drove for 1.9 hours.

How many hours did Carlos drive for? well, c = 4.1 - m.

4 0

3 years ago

ANYONE PLEASE HELP!!!

VashaNatasha [74]

The answer is provided in the photo below:

8 0

3 years ago

10. Sarah finances $549,000 with a 30/6 balloon mortgage at 5.35%. How much will she pay for principal and interest over the lif

topjm [15]

Answer:

$717,393.12

Step-by-step explanation:

The 30/6 balloon mortgage means that she would make monthly payments for the first six years, while the balance outstanding after 6 years is paid by making one large payment.

The 30 implies that monthly payment should be computed on the basis it is a 30-year mortgage.

Loan amount=monthly payment*(1-(1+r)^-n/r

loan amount=$549,000

monthly payment=the unknown

r=monthly interest rate=5.35%/12=0.004458333

n=number of monthly payments in 30 years=30*12=360

549000=monthly payment*(1-(1+0.004458333)^-360/0.004458333

549000=monthly payment*(1-0.201607475)/0.004458333

549000=monthly payment*0.798392525/0.004458333

monthly payment=549000*0.004458333/0.798392525=$ 3,065.69

Total monthly payments for6 years=$ 3,065.69*12*6=$220,729.68

The ballon payment is the present value of monthly payments for 24 years remaining

Financial calculator:

N=288(24*12)

PMT=3065,69(monthly payment)

I/Y=5.35/12(monthly interest rate)

FV=0(balance after payments is nil)

CPT PV=$496,663.41

Total payments=$496,663.41 +$220,729.68=$717,393.09

6 0

2 years ago